1. and 2. Depends heavily on the patent classification and seniority. I get around 20-25 hours for a first action, much less for subsequent actions. I'm a newbie, though. Primary examiners in my area probably get only about 10-13 hours for a first action. The time I get is for both search and examination.
Comprehensiveness varies and can be independent of whether other offices have done searches. It can be hard to get even two examiners at the same office to agree on what good prior art is. I've inherited applications from an examiner who retired and I didn't always agree with their prior art.
I tend to use foreign searches as starting points for my own searches. I'd guess about half the time what I find is the same as the foreign search or comparable but different. Often I find clear deficiencies in foreign searches.
The time I get does not change if there are foreign actions. I get so little time that I hesitate to even write the previous sentence in case it gives upper management ideas about where to reduce time...
Searching at patent offices is never particularly comprehensive in my experience. If someone wants a comprehensive search, their main option is to do it themselves.
3. I am required to do at least a cursory search after any amendment as far as I'm aware. How detailed the search is varies. See the next point for how much time I get.
4. I get about 4 hours for a final rejection. The US has "after-final" actions as well which can provide up to 3 hours if I recall correctly, but are much more limited in scope and rarely used properly by applicants in my experience. After-final actions should be used mainly to cancel any claims not declared allowable by the examiner, in my opinion.
5. All USPTO examiners have classification as one of their duties now, but they are given very little time for this. The time varies between 0 time, 30 minutes, and 1 hour depending on the results of an approval process.
Longer version: The USPTO recently made some significant changes to classification and docketing. Applications are docketed to examiners based on a combination of the CPC and USPC classification now, with the eventual goal of eliminating the USPC component of the docketing system. Here's how it works: Poorly paid contractors classify patent applications. Based on the classification from the contractors, applications are docketed to examiners. Examiners then have the opportunity to correct the classification if it's wrong. As it turns out, poorly paid contractors don't classify well. I'd guess that about 10% of the applications I'm docketed have serious classification issues. The precise number probably varies appreciably between examiners. I will try to correct the classification issues with a process called a C* challenge. This requires approval by examiners called SCEs. The SCEs will check if they agree with the examiner's proposed classification. Sometimes they'll add their own classification, but usually not. The amount of time an examiner gets is zero if none of the changes are approved, 30 minutes if the changes are approved but the changes do not cause the application to be transferred from the examiner, and 1 hour if the changes are approved and the changes cause the application to be transferred. Unfortunately, properly classifying applications frequently takes far longer than 1 hour. This is particularly true when examiners have to classify applications in areas they know little about.
I don't bother changing the classification at this point if it seems mostly right because the amount of time I get for correcting the classification is so small. I will only try to correct the classification if it's egregiously wrong.
6. I think I saw some screenshots of the EPO's software once, but I don't really know how it compares to what the USPTO uses. For what it's worth, the USPTO's new public search tool is very similar to the internal tool. The main difference is that the USPTO decided to only include US patent documents in the public version, which is a shame. https://ppubs.uspto.gov/pubwebapp/static/pages/landing.html
(Again, like my other comments here, this is just my opinion, not that of the USPTO or US government.)